Knots and Primes
Author: Masanori Morishita
Publisher: Springer Nature
Published:
Total Pages: 268
ISBN-13: 9819992559
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Knots and Primes
Author: Masanori Morishita
Publisher: Springer Science & Business Media
Published: 2011-11-27
Total Pages: 192
ISBN-13: 1447121589
DOWNLOAD EBOOK →This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Primes and Knots
Author: Toshitake Kohno
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 298
ISBN-13: 0821834568
DOWNLOAD EBOOK →This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.
The Knot Book
Author: Colin Conrad Adams
Publisher: American Mathematical Soc.
Published: 2004
Total Pages: 330
ISBN-13: 0821836781
DOWNLOAD EBOOK →Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Knots and Links
Author: Dale Rolfsen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 458
ISBN-13: 0821834363
DOWNLOAD EBOOK →Rolfsen's beautiful book on knots and links can be read by anyone, from beginner to expert, who wants to learn about knot theory. Beginners find an inviting introduction to the elements of topology, emphasizing the tools needed for understanding knots, the fundamental group and van Kampen's theorem, for example, which are then applied to concrete problems, such as computing knot groups. For experts, Rolfsen explains advanced topics, such as the connections between knot theory and surgery and how they are useful to understanding three-manifolds. Besides providing a guide to understanding knot theory, the book offers 'practical' training. After reading it, you will be able to do many things: compute presentations of knot groups, Alexander polynomials, and other invariants; perform surgery on three-manifolds; and visualize knots and their complements.It is characterized by its hands-on approach and emphasis on a visual, geometric understanding. Rolfsen offers invaluable insight and strikes a perfect balance between giving technical details and offering informal explanations. The illustrations are superb, and a wealth of examples are included. Now back in print by the AMS, the book is still a standard reference in knot theory. It is written in a remarkable style that makes it useful for both beginners and researchers. Particularly noteworthy is the table of knots and links at the end. This volume is an excellent introduction to the topic and is suitable as a textbook for a course in knot theory or 3-manifolds. Other key books of interest on this topic available from the AMS are ""The Shoelace Book: A Mathematical Guide to the Best (and Worst) Ways to Lace your Shoes"" and ""The Knot Book.""
Knots
Author: Alekseĭ Bronislavovich Sosinskiĭ
Publisher: Harvard University Press
Published: 2002
Total Pages: 158
ISBN-13: 9780674009448
DOWNLOAD EBOOK →This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.
High-dimensional Knot Theory
Author: Andrew Ranicki
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 669
ISBN-13: 3662120119
DOWNLOAD EBOOK →Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
Introduction to Knot Theory
Author: R. H. Crowell
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 191
ISBN-13: 1461299357
DOWNLOAD EBOOK →Knot theory is a kind of geometry, and one whose appeal is very direct because the objects studied are perceivable and tangible in everyday physical space. It is a meeting ground of such diverse branches of mathematics as group theory, matrix theory, number theory, algebraic geometry, and differential geometry, to name some of the more prominent ones. It had its origins in the mathematical theory of electricity and in primitive atomic physics, and there are hints today of new applications in certain branches of chemistryJ The outlines of the modern topological theory were worked out by Dehn, Alexander, Reidemeister, and Seifert almost thirty years ago. As a subfield of topology, knot theory forms the core of a wide range of problems dealing with the position of one manifold imbedded within another. This book, which is an elaboration of a series of lectures given by Fox at Haverford College while a Philips Visitor there in the spring of 1956, is an attempt to make the subject accessible to everyone. Primarily it is a text book for a course at the junior-senior level, but we believe that it can be used with profit also by graduate students. Because the algebra required is not the familiar commutative algebra, a disproportionate amount of the book is given over to necessary algebraic preliminaries.
Knot Theory
Author: Charles Livingston
Publisher: Cambridge University Press
Published: 1993
Total Pages: 276
ISBN-13: 9780883850275
DOWNLOAD EBOOK →This book uses only linear algebra and basic group theory to study the properties of knots.
Knots
Author: Gerhard Burde
Publisher: Walter de Gruyter
Published: 2013-11-27
Total Pages: 432
ISBN-13: 3110270781
DOWNLOAD EBOOK →This 3. edition is an introduction to classical knot theory. It contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known.
